Three-Phase Power Calculator

Enter the line-to-line voltage, power factor and one known quantity (line current, active power in kW, or apparent power in kVA) to calculate the full three-phase power triangle.

Fill voltage, power factor and one known value.

How It Works

The three-phase power triangle

Three-phase AC systems carry three quantities of power, related by the power triangle:

  • S (kVA, apparent power) = √3 × VL × I
  • P (kW, active power) = S × pf
  • Q (kVAR, reactive power) = √(S² − P²)

Solving from each known

  • From current: S = √3 × V × I; then P = S × pf
  • From kW: P = kW × 1000; S = P / pf; I = S / (√3 × V)
  • From kVA: S = kVA × 1000; P = S × pf; I = S / (√3 × V)

Worked example

With V = 400 V, pf = 0.8 and line current = 10 A:

  • S = √3 × 400 × 10 = 6,928 VA (6.928 kVA)
  • P = 6,928 × 0.8 = 5,543 W (5.543 kW)
  • Q = √(6,928² − 5,543²) ≈ 4,157 VAR (4.157 kVAR)

Three-Phase Power Reference

Common voltages

208 V (US 3-ph low)
380 V (IEC/EU)
400 V (IEC/EU)
415 V (UK)
480 V (US industrial)

Line vs neutral

VL-N = VL-L / √3
e.g. 400 V L-L ≈ 231 V L-N
e.g. 480 V L-L ≈ 277 V L-N

Power factor guide

Resistive loads: pf = 1.0
Motors: pf 0.7 to 0.9
Fluorescent: pf ~0.85
Ideal target: pf ≥ 0.95

Frequently Asked Questions

What is the three-phase power triangle?

The power triangle shows how active power (kW), reactive power (kVAR) and apparent power (kVA) relate in an AC circuit. kVA is the hypotenuse, kW is the adjacent side, and kVAR is the opposite side. The power factor equals kW divided by kVA, which is the cosine of the angle between them.

What is the difference between kW, kVA and kVAR?

kW (kilowatts) is real, active power that does useful work. kVA (kilovolt-amperes) is apparent power, the product of voltage and current. kVAR (kilovolt-amperes reactive) is the reactive power consumed by inductors and capacitors. The relationship is: kVA² = kW² + kVAR².

Why does the three-phase formula use the square root of 3?

In a balanced three-phase system, the total power is the vector sum of three equal single-phase contributions displaced by 120 degrees. When you express this using the line-to-line voltage, the geometry works out to a factor of √3 (approximately 1.732). For single-phase, the factor is simply 2 (one conductor out, one return).

What is the difference between line-to-line and line-to-neutral voltage?

Line-to-line (L-L) voltage is measured between any two of the three phase conductors; line-to-neutral (L-N) voltage is measured from one phase to the neutral. They are related by VL-L = √3 × VL-N. This calculator uses line-to-line voltage because that is the value used in the three-phase power formula S = √3 × VL-L × I.

How do I find the three-phase line current from kW?

Rearrange S = √3 × V × I to get I = S / (√3 × V). Since S = P / pf = kW × 1000 / pf, the formula becomes I = (kW × 1000) / (√3 × V × pf). For example, a 5.543 kW load at 400 V and pf 0.8 draws I = 5543 / (1.732 × 400 × 0.8) = 10 A.

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